Surface profiling is an important need in many industrial and scientific applications. Typical examples include flatness inspection of railway rails and road surfaces, and quality control of manufactured products such as sawn lumber and rolled metal.
The simplest way to measure surface height profile is to make a series of measurements with a distance sensor while relatively moving the measured object and the sensor in a straight line perpendicular to the measurement direction. FIG. 1(a) schematically shows an example arrangement. The drawback to this method is that deviations from straight-line motion cause relative displacements in the measurement direction that are indistinguishable from measured surface shape. Thus, very accurate linear motion is essential.
In many cases, accurate linear motion is not practicable. For example, when measuring the surface profile of a long length of railway track, it is not feasible to provide a separate linear slide for moving the sensor. Instead, the sensor must travel on the irregular track that it is measuring. Existing non-inertial techniques focus on the surface curvature because it can be identified independently of relative displacements or rotations. A typical arrangement uses three or more sensors operating simultaneously, as shown in FIG. 1 (b). U.S. Pat. No. 4,288,855 describes examples of this concept. The sensors estimate the local surface curvature from the second finite difference of their measurements. The curvature values are integrated twice to determine the surface profile. This method is effective, but it has difficulty resolving surface features that are either greatly shorter or greatly longer than the total spacing of the sensors.
U.S. Pat. No. 5,280,719 describes an apparatus that uses a large number of equally spaced sensors. The apparatus seeks to identify long surface features by overlapping sets of measurements that are made at successive intervals much less than the total spacing of the sensors. However, the large number of sensors that are required creates a large cost and maintenance burden. U.S. Pat. No. 4,573,131 describes a method of using just four sensors to achieve the same objective. The sensors make successive measurements at small intervals of travel. The sensor spacings are chosen so that the numbers of intervals of travel between successive sensors have no common factors other than unity. This feature avoids the existence of “nulls”, which is a measurement artifact whereby surface features with specific wavelengths are not observed. The method described in U.S. Pat. No. 4,573,131 is based on the assumption that successive sensors reaching the same point along the measured line have the same distance from the measured surface. This is typically not a reasonable assumption, and the described method has only limited effectiveness.
An alternative approach, the “inertial” method, uses an accelerometer that runs at a constant speed along the surface to be profiled, giving a signal that is proportional to surface curvature. This signal is integrated twice to obtain the surface shape. Conceptual simplicity makes this an attractive method. However, there are also some practical limitations. The first concerns the high frequencies that need to be measured. These can extend beyond the capabilities of the accelerometer. A second limitation is the assumption that the accelerometer and the surface are permanently in contact. This is difficult to achieve reliably, especially at high scanning speeds due to the large inertial forces that act on the system. Finally, only smooth profiles can be measured. A sharp step, for example, would not be detected properly.
None of the above techniques is well suited to measuring the surfaces of two-sided objects. At best, they can measure each of the two sides separately, but they do not provide accurate thickness information. Similarly, they do not provide accurate twist information with parallel measurements, nor are they suitable for two-dimensional surface evaluations.